U.S. Pat. No. 6,758,188, entitled “Continuous Torque Inverse Displacement Asymmetric Rotary Engine”, the disclosure of which is incorporated herein by reference, discloses an Inverse Displacement Asymmetric Rotary (IDAR) engine. The engine includes an inner chamber wall, an outer chamber wall, and a movable contour defined by the following discussion.
Torque can be achieved throughout a combustion cycle by designing a chamber in a rotary engine such that an angle of incidence between a direction of force from a concave-shaped contour and a direction of force of an outer chamber wall at every point along the outer chamber wall during the combustion cycle is some angle greater than (0) degrees and less than (90) degrees. The shape of an inner chamber wall, the outer chamber wall, and the concave-shaped contour that are conducive to an angle of incidence between (0) degrees and (90) degrees can be determined algebraically with regard to a predetermined angle of incidence.
As illustrated in FIG. 1, with S representing a chamber wall surface and CS representing a crankshaft, the amount of torque generated by a pre-determined angle of incidence C created by a force F(r) interacting with a surface can be equal to F(r)*distance D*cos(C)*sin(C). As can be determined mathematically, torque is at a maximum value when the angle of incidence C is (45) degrees. The value of cosine*sine for a (45) degree angle is equal to (0.5). Other angles of incidence between about (20) degrees and about (70) degrees can generate suitable amounts of torque.
As shown in FIG. 2, if a radius R were held constant as it rotated through some angle D about a point CS, a tangent C to an arc described by the radius R would define a straight line between points X and Z. Tangent C makes a right angle with respect to the radius at the center of the arc (angle D/2). If line X-Z also described a surface of a chamber against which the radius was pushing, at angle D/2, the angle of incidence between a direction of force from the radius and a direction of force from the surface would be (0).
This relation describes a condition in traditional rotary engine technology, wherein the angle of incidence is (0) at the beginning and at the end of a combustion cycle. In order to achieve torque during all of the combustion cycle, the angle of incidence can be between (0) and (90) degrees at every point during the combustion cycle.
FIG. 3 depicts a tangent C between points Y and Z to an arc generated by rotation of a changing radius through some angle D about a fixed point CS. If tangent C is a surface against which the changing radius pushes, the angle of incidence between a direction of force from the radius and a direction of force from the surface would be angle E, which is some angle between (0) degrees and (90) degrees.
The changing radius length at any given point in FIG. 3 can be equal to R+dR, wherein R is a starting radius length, and dR is a variable length equal to or greater than 0. If the values of R and dR are known over an angle D, angle of incidence E can be calculated. Conversely, if angle of incidence E is known for the midpoint D/2 of some angle of rotation D, the length dR can be determined.
A mathematical formula for a curve can be derived wherein the radius of the curve makes an angle of incidence greater than 0 degrees and less than (90) degrees with a surface at every point along the curve as the radius rotates about a fixed point of rotational reference. The angle of incidence can be between about (20) degrees and about (70) degrees at every point along the curve. The mathematical formula can be used to derive a curve that can be the profile of a movable contour and a portion of a stationary inner chamber wall of the IDAR.
With continued reference to FIG. 3, a pre-determined angle of incidence E can be used to calculate an amount dR by which a radius R has to increase to maintain angle of incidence E as the radius (R+dR) rotates about a crankshaft. For an angle of incidence E of (45) degrees, the triangle XYZ in FIG. 3 has legs XY and XZ of equal length. The formulae for determination of the change in radius dR in relation to the radius R necessary to create angle of incidence E of 45 degrees are:dR*(cos(D/2))=DR*sin(D/2))+2*R*sin(D/2)  (2)dR*(cos(D/2)−sin(D/2))=2*R*sin(D/2)  (4)dR/R=2*sin(D/2)/*(cos(D/2)−sin(D/2))  (6)
Formula (6) indicates that for a given angle of rotation D, for example, (1) degree, the radius R must change by a certain percentage, equal to length dR. The percentage R must change, dR/R, is constant in order to maintain a constant angle of incidence E of (45) degrees over some angle of rotation D. The percentage change can be an increase in length. For example, using Formula (6), for a (45) degree angle of incidence E to be generated over (1) degree of rotation, the radius R can increase by about 1.76%. The percentage by which R changes (dR) can remain constant regardless of the initial value of R for each degree of rotation.
A generic formula for angles other than 45 degrees can be generated by multiplying the right side of Formula (6) by a scaling factor K. Scaling factor K is the difference in the length of leg XY of triangle XYZ as compared to the length of leg XZ when the angle of incidence E is changed from (45) degrees, wherein the lengths XY and XZ are equal. When angle of incidence E is not (45) degrees, the formula is:dR/R=2*sin(D/2)/(K*cos(D/2)−sin(D/2))  (8)
The scaling factor K is equal to 1/tan(E). When angle E is (45) degrees, 1/tan(45)=1, resulting in Formula (6). Where angle E is not (45) degrees, K has some value not equal to (1). Formula (8) can be used to calculate by what percentage R must change over a degree of rotation D to generate a pre-determined angle of incidence E.
A curve generated by Formula (6) or (8) using a constant angle of incidence E can rapidly spiral outward from a fixed point of rotation. For a less aggressive spiral with a smaller percentage change in radius, a changing angle of incidence E can be used. For example, the angle of incidence at the beginning of the curve can be (45) degrees or greater and less than (90) degrees, and can decrease gradually as R rotates about a fixed point. A changing angle of incidence, for example a continuously decreasing angle of incidence, can be maintained between (90) degrees and (0) degrees, or between (70) degrees and (20) degrees.
Referring to Formula (2) with relation to FIG. 3, it can be seen that the term dR*sin(D/2) defines a very small value in relation to the other terms of the formula. If term dR*sin(D/2) were subtracted from, instead of added to, term 2*R*sin(D/2), the value of the radius R would still be increasing, but more gradually, and the angle of incidence E would be gradually decreasing. Subtracting term dR*sin(D/2) from term 2*R*sin(D/2) and scaling by scaling factor K for a starting angle of incidence other than (45) degrees results in the following formula:dR/R=2*R*sin(D/2)/(K*cos(D/2)−sin(D/2))  (10)
Using the above Formula (10) with a starting radius length R of (2) and a starting angle of incidence E of (45) degrees, K would be equal to (1), and a curve as shown in FIG. 4 would be generated.
FIG. 4 depicts an exemplary curve generated by Formula (10), as well as a graph of two circles, one with a radius equal to (1) unit and one with a radius equal to (2) units. With continued reference to FIG. 4, a line drawn from the origin to a tangent at any point on the curve generated according to Formula (10) will have an angle of incidence of (45) degrees at (0) degrees of rotation, and the angle of incidence will gradually decrease to about (20) degrees at (90) degrees of rotation.
An inner chamber wall of the IDAR having the contour of the curve of FIG. 4 can be generated, which can result in an angle of incidence with a concave-shaped contour beginning at (45) degrees at (0) degrees of rotation and gradually decreasing to about (20) degrees at (90) degrees of rotation. Because a contour of an outer chamber wall of the IDAR can be a function of the contour of the inner chamber wall, the angle of incidence between a direction of a component of force generating torque from the concave-shaped contour and a force of the outer chamber wall will also vary from (45) degrees to about (20) degrees during the combustion cycle.
In order to form an inner chamber wall contour, a curve generated by Formula (10), for example the curve shown in FIG. 4, can be repeated and rotated (180) degrees to form two intersecting curves of the same shape, as shown in FIG. 5. The shape generated in FIG. 5 can define an inner chamber wall of the IDAR and an island about which a concave-shaped contour of the IDAR can rotate within a chamber of the IDAR. The point of origin of the curve generated by Formula (10) can be a location of a crankshaft within the island of the IDAR. As shown in FIG. 5, the crankshaft can be off-center within the island of the IDAR. A concave-shaped contour that mates with the shape of the inner chamber wall can be generated, as shown in FIG. 6.
A chamber 2 with a concave-shaped contour 4, as exemplified in FIG. 6 can have crank pivot 6 and retainer 8 off-set in relation to a center of inner curve 10. The position of crank pivot 6 and retainer 8 can be offset, towards one side of the contour, as compared with a geometric center of the contour.
The shape of the outer chamber wall 14 can be generated by moving a concave-shaped contour around an inner chamber wall. The outside chamber wall can be designed so as to hold the concave-shaped contour against the inner chamber wall while the retainer or outer curve of the concave-shaped contour moves along the outer chamber wail. Accordingly, FIG. 6 depicts that, within the chamber 2, the contours and/or position of an inner chamber wall 16, an island 18, the crankshaft 12, the outer chamber wall 14, the concave-shaped contour 4, the crank pivot 6 and the retainer 8 is determined in relation to the curve generated by Formula (10).
It can be appreciated by visual inspection of FIG. 6 that the shape of the outer chamber wall 14 can be derived from the same mathematical function as the inner chamber wall 16. The outer chamber wall 14 can have the same shape as at least a portion of the inner chamber wall 16, but larger in scale and rotated by some angle, for example (90) degrees, about an origin during a portion of chamber 2 that corresponds to the combustion cycle.
The above described IDAR engine technology has many advantages over typical internal combustion piston engine technology. Some of the advantages that the IDAR geometry provides are different size cycle lengths.
For instance, the compression cycle can occur in a shorter stroke distance than the expansion (combustion) cycle. This allows for more work to be extracted during the longer expansion cycle when compared to piston technology of the same displacement.
Similarly, the exhaust and intake cycles do not have to be the same length either. The expansion cycle of the IDAR engine also has a mechanical transfer function into work that is nearly continuous instead of the bell curve transfer function of piston technology. This translates into a torque curve that is very flat with little variation across the rpm range. This occurs partly because the crank arm, in effect, grows in length as the expansion cycle progresses.
Also, all four of the engine cycles: intake, compression, combustion and exhaust, can have different lengths and different volumes and can occur at different rates within the same four-stroke sequence. This allows IDAR engine designers to optimize engine performance and reduce pollution by-products in a way that is superior to piston engine technology.
In addition, all four cycles occur within one complete rotation of the shaft. The IDAR engine performs somewhat like a two-cycle engine in that it has very high acceleration rates but, at the same time, it has the torque generation characteristics of a long stroke diesel engine of similar displacement. The IDAR engine geometry should not be grouped into sub-categories of performance based on bore-to-stroke ratios, as is done with piston technology, because the IDAR spans all of those categories when similar comparisons are made.
In the actual fabrication of an IDAR engine, there are complex curves and flat surfaces. The seals, however, always seal against a surface that is flat and oriented in the direction of the length of the seal material. This means that the critical manufacturing dimension is the flatness of the surfaces of the parts and the ability to align parts, such that opposite sides are parallel across the width of the engine. It is also important that parts do not twist in the direction of the path of movement and that surfaces which start off perpendicular to one another remain perpendicular to one another during the combustion cycle.
Because the cycle lengths, volumes, and rates can be different from each other and are not symmetric as in piston engine technology, it is important to have good port flow control during intake and exhaust. This allows performance standards that are beyond piston engine technology capabilities to be met.
In addition, because the IDAR engine has a unique expansion stroke, the geometry lends itself to basic power plant design based only on the expansion stroke of the IDAR. When an IDAR is connected to an external apparatus, it forms an external combustion engine or power plant powered by some other propellant, such as compressed air.
An object of the invention is to provide improvements to IDAR technology control, performance, ease of manufacture and the expansion of use of the IDAR technology.